Question: Simplify; express your answer in exponential form. Assume $p\neq 0, r\neq 0$. $\dfrac{{(p^{-1}r^{5})^{-5}}}{{(pr^{-2})^{4}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(p^{-1}r^{5})^{-5} = (p^{-1})^{-5}(r^{5})^{-5}}$ On the left, we have ${p^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(p^{-1})^{-5} = p^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{(p^{-1}r^{5})^{-5}}}{{(pr^{-2})^{4}}} = \dfrac{{p^{5}r^{-25}}}{{p^{4}r^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{5}r^{-25}}}{{p^{4}r^{-8}}} = \dfrac{{p^{5}}}{{p^{4}}} \cdot \dfrac{{r^{-25}}}{{r^{-8}}} = p^{{5} - {4}} \cdot r^{{-25} - {(-8)}} = pr^{-17}$